Two points are chosen at
random in the interval [0, 1]; X denotes the first point chosen and Y denotes
the second point chosen. Random variable U gives the type of triangle that can
be formed from the three sub-intervals:
- U = 0: the pieces do not form a triangle.
- U = 1: the pieces form an obtuse triangle.
- U = 2: the pieces form an acute triangle.
- U = 2 consists of the 2 interior regions.
- U = 1 consists of the 6 middle regions.
- U = 0 consists of the outer regions.
Software/Applets used on this page

an applet from PSOL from UAH
Glossary
acute
An angle less than 90 degrees.
cut
A set of edges whose removal separates a network into two parts, where one part contains the source and the other part contains the sink.
density
the ratio of the mass of an object to its volume
function
A rule that connects one value in one set with one and only one value in another set.
graph
A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.
The diagram shows a vertical y axis and a horizontal x axis.
obtuse
an angle between 90 and 180 degres
random variable
a variable that represents the values obtained when measurements are taken from a population in the real world; it must take a numerical value.
sample space
The list of all possible outcomes from an experiment.
variable
A value which is unknown and free to vary, often denoted by x or y.
This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |
CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |
CCEA A-Level (NI) | S1 | Probability | Experimental | - |
CIE A-Level (UK) | S1 | Probability | Experimental | - |
Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
I.B. Higher Level | 5 | Probability | Experimental | - |
I.B. Standard Level | 5 | Probability | Experimental | - |
Methods (UK) | M15 | Probability | Experimental | - |
I.B. (MSSL) | 3 | Probability | Experimental | - |
OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
Pre-Calculus (US) | E4 | Probability | Experimental | - |
Pre-U A-Level (UK) | Prob | Probability | Experimental | - |
Scottish (Highers + Advanced) | HS | Probability | Experimental | - |
Scottish Highers | S | Probability | Experimental | - |
Universal (all site questions) | P | Probability | Experimental | - |
WJEC A-Level (Wales) | S1 | Probability | Experimental | - |